Simplify:
(4.2)3 − (1.2)3⁄(4.2)2 + 5.04 + (1.2)2
3
Step 1: Recall the identity for cubes
The numerator follows the identity:
a3 − b3 = (a − b)(a2 + ab + b2)
Here, a = 4.2 and b = 1.2.
Numerator = (4.2 − 1.2)((4.2)2 + (4.2 × 1.2) + (1.2)2)
= (3)((4.2)2 + (4.2 × 1.2) + (1.2)2).
Step 2: Simplify the numerator
(4.2)2 = 17.64, (4.2 × 1.2) = 5.04, (1.2)2 = 1.44.
Numerator = (3)(17.64 + 5.04 + 1.44) = (3)(24.12) = 72.36.
Step 3: Simplify the denominator
Denominator = (4.2)2 + 5.04 + (1.2)2
= 17.64 + 5.04 + 1.44 = 24.12.
Step 4: Calculate the result
Result = Numerator ÷ Denominator = 72.36 ÷ 24.12 = 3.
Thus, the correct answer is 3.
Similar Questions
2 biscuits and 1 chocolate cost ₹69.
2 chocolates and 3 cups of coffee cost ₹127.
3 biscuits, 4 chocolates, and 2 cups of coffee cost ₹229.
Find the total cost (in ₹) of 5 biscuits, 5 chocolates, and 5 cups of coffee.
If 0.4x + 0.16y = 1.7 and 0.3x + 0.12y = 3.4, then which of the following is correct?
The value of the expression (1.552 + 0.552 + 1.55 × 0.55) is equal to:
Find the value of Y, if X - 2Y + 2Z = 16, X - Y + Z = 9 and 2X - 3Y - Z = 9.
For which of the following values of a and b do the given equations have NO solution?
x − ay = 2 − a
(1 − a)x + 6y = a + b- If $P + Q = 2R$ and $R + S = 2P$, then:
- Find the solution to the system: $y = 3x - 4$ and $y = -x + 2$.
The solution of the following equations is:
5x + 4y - 8z = 1
7x - 9y + z = -1
2x + 3y - 4z = 1
The sum of two numbers is 40 and their difference is 4. What is the product of the numbers?
If 3x - ky + 8 = 0 and 9x - 18y + 20 = 0 have no solution, find k.
Important Questions from Linear Equation in 2 or more Variables
If \(3x+6y+9z = \dfrac{20}{3}, 6x+9y + 3z = \dfrac{17}{3}\) and \(18x+ 27y - z = \dfrac{113}{9}\) , then what is the value of \(75x+113y \ ?\)
If the system of equations 2x - 3y - 3 and -4x + qy - p/2 is inconsistent which of the following cannot be the value of p ?
If \(4x + \dfrac{6}{y}= 15 \) and \(6x - \dfrac{8}{y} = 14\) , then the value of p in y = px - 2 is :
Simplify: 7x + 3x(x – 4) = ?
A. 10x + 12
B. 10x – 12
C. 3x2 + 5x
D. 3x2 – 5xIf 5x + y = 17 and xy = 6, then what is the value of 125x3 + y3 ?
